Solve for $x$ and $y$ using elimination. ${3x+4y = 25}$ ${2x-y = 2}$
Solution: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Multiply the bottom equation by $4$ ${3x+4y = 25}$ $8x-4y = 8$ Add the top and bottom equations together. $11x = 33$ $\dfrac{11x}{{11}} = \dfrac{33}{{11}}$ ${x = 3}$ Now that you know ${x = 3}$ , plug it back into $\thinspace {3x+4y = 25}\thinspace$ to find $y$ ${3}{(3)}{ + 4y = 25}$ $9+4y = 25$ $9{-9} + 4y = 25{-9}$ $4y = 16$ $\dfrac{4y}{{4}} = \dfrac{16}{{4}}$ ${y = 4}$ You can also plug ${x = 3}$ into $\thinspace {2x-y = 2}\thinspace$ and get the same answer for $y$ : ${2}{(3)}{ - y = 2}$ ${y = 4}$